75368 - Statistics

Learning outcomes

At the end of the course, students will have acquired knowledge of the main statistical techniques for exploratory data analysis and for inference of population parameters from random samples. The learnt techniques cover graphical tools, summary measures for single and multiple variables, estimation and hypothesis testing for Gaussian and Binomial populations. Students will also be able to implement some of the taught techniques through the statistical software R. Skills to solve elementary probability problems will be developed.

Course contents

The course program is organized in four parts as described below.

1. Exploratory data analyis
Graphical tools for data analysis and presentation. Frequency tables. Frequency distributions. Summary measures of position and dispersion. Two-way contingency tables. Joint, marginal and conditional distributions. Independence. Association and chi-squared index. Linear dependence and correlation. Outline of simple linear regression models.

2. Probability Theory
Approaches to Probability Theory. Axiomatic approach to probability. Sets and Events. Conditional probability. Independent events. Total probability theorem. Random variables. Mean, quantiles and variance. Discrete and Continuous Uniform distribution. Binomial distribuiton. Gaussian distribution. Independent variables. Sums of random variables. Central limit theorem and related corollaries. Chi-squared and t distributions.

3. Inferential Statistics
Random sampling. Parametric statistical models. Sampling distributions. Point estimation. Bias and mean squared error. Confidence intervals for the mean of a Gaussian population. Approximate confidence interval for a probability. Confidence interval for the difference between the means of two Gaussian populations. Hypothesis testing on the mean of a Gaussian population. The p-value. Approximate test on a probability. Test on the difference between the means of two Gaussian populations.Approximate test of independence on a two-way table.

 

4. Computer programming
Some lectures will be held in the computer laboratory where students will be introduced to the use of R, a free software for statistical computing and graphics. Through R the acquired statistical techniques will be applied to real-life problems.

 

Readings/Bibliography

• Anderson, D.R., Sweeney, D.J., Williams, T.A., Camm, J.D. and Cochran, J.J. (2014), Statistics for Business and Economics, Cengage Learning, Stamford, CT, USA. 12th Edition.           

• Lecture notes that will be available at the web page http://www2.stat.unibo.it/bortot/default.html at the beginning of the course.

Teaching methods

Traditional lectures and computer laboratory sessions.

Assessment methods

Written examination. In some cases, after the written exam, the lecturer may require an oral exam as a further tool of assessment of the student's preparation.

Teaching tools

The statistical software R, which will be used in the laboratory sessions, can be freely downloaded from the web page http://www.r-project.org/

Links to further information

http://www2.stat.unibo.it/bortot/default.html

Office hours

See the website of Paola Bortot